Solve for x -3<=4x+9<=17

$- 3 \leq 4 x + 9 \leq 17$

Step 1

Move all terms not containing $x$ from the center section of the inequality.

Subtract $9$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 3 - 9 \leq 4 x \leq 17 - 9$

Subtract $9$ from $- 3$ .

$- 12 \leq 4 x \leq 17 - 9$

Subtract $9$ from $17$ .

$- 12 \leq 4 x \leq 8$

Step 2

Divide each term in the inequality by $4$ .

$\frac{- 12}{4} \leq \frac{4 x}{4} \leq \frac{8}{4}$

Step 3

Divide $- 12$ by $4$ .

$- 3 \leq \frac{4 x}{4} \leq \frac{8}{4}$

Step 4

Cancel the common factor of $4$ .

Cancel the common factor.

$- 3 \leq \frac{4 x}{4} \leq \frac{8}{4}$

Divide $x$ by $1$ .

$- 3 \leq x \leq \frac{8}{4}$

Step 5

Divide $8$ by $4$ .

$- 3 \leq x \leq 2$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 3 \leq x \leq 2$

Interval Notation:

$[- 3, 2]$

Step 7